Quantum mechanics uses two important concepts we usually are not aware of in daily life: the principle of least action (as classical mechanics does) and wave functions with amplitudes, which leads to a probability density according to Born's rule. There is a third concept evolving from those: Feynman's path integral method mimics Fermat's principle.
WP: Fermat's principle WP: Action principles WP: Path integral formulation WP: Wave function WP: Probability amplitude WP: Born rule